Is there any Python library available for manifold learning using diffusion map?
The first place I would have directed you would be Sklearn and pydiffmap. I found this paper specifically about the problem you are doing using python the reference a package called  megaman  It seems like an active  Github . I suggest not just looking at manifold learning papers but leaning towards a search toward non linear embedding or non linear dimensionality reduction as well. The paper you give doesn't reference local linear embedding but seems to be similar conceptually. 

I found this   kernel pca document  which is very straight forward and I think will help you going forward as well. I believe the RBF Kernel PCA part may be of use to you at least as a way of benchmarking how well your diffusion map is functioning.